Jong-In Shim and Dong-Soo Shin* Measuring the internal

Nanophotonics 2018; 7(10): 1601–1615

Review article

Jong-In Shim and Dong-Soo Shin*

Measuring the internal quantum efficiency of light-emitting diodes: towards accurate and reliable room-temperature characterizationhttps://doi.org/10.1515/nanoph-2018-0094Received July 11, 2018; revised August 20, 2018; accepted August 20, 2018

Abstract: For accurate and reliable measurement of the internal quantum efficiency (IQE) of light-emitting diodes (LEDs), the method should be theoretically solid and experimentally simple to use without any prior assumption of physical parameters or compli-cated equipment. In this paper, we critically review the conventional characterization techniques for measur-ing the IQE of LEDs, including the methods based on temperature-dependent electroluminescence and con-stant AB(C) models. After reviewing the limitations of the existing IQE measurement techniques, we present the recently proposed method based on the improved AB model, called room-temperature reference-point method (RTRM). The RTRM is then applied to various LED devices to show how the IQE measurement tech-niques can be utilized to analyze their optoelectronic performances quantitatively.

Keywords: light-emitting diodes; internal quantum effi-ciency; characterization.

1 IntroductionNowadays, light-emitting diodes (LEDs) are found in numerous applications for their many advantages such as low power consumption, small size, long lifetime,

and fast switching. LEDs are available in various spec-tral ranges including ultraviolet, visible, and infrared wavelengths, based on different material systems [1–3]. Wide-bandgap materials such as GaN and associated alloys have been actively studied recently to achieve blue and UV emissions. While the LEDs are composed of simple pn junctions, there can exist multiple issues related with device configurations and materials. In order to analyze any possible device issues, accurate characterization of the device performance is an abso-lute necessity.

Many parameters have been utilized for LED devices to quantify the device performance so far: parameters obtained from simple current-voltage (I-V) and light- current (L-I) measurements constitute a basis, but they do not typically give enough details about a device under study [4–11]. Since many device parameters are interrelated, more extensive characterization is required to form a complete picture of the possible cause of the problem in the device and remedy it [12, 13]. At the same time, if there is any measure introduced to remedy and enhance the device performance, it is sometimes very difficult to judge whether the intended effects are achieved by simply checking the output parameters such as I-V and L-I.

Of the various device parameters, efficiencies contain the most important information on the device performance and any possible problem. Typically, the overall efficiency of the LED device is characterized by the power efficiency (PE), ηPE, defined by the ratio of the radiant power (optical power) from the LED to the input electrical power. The PE is rather simple to measure and serves as a useful parameter representing how efficient the device is in converting the electrical power to the desired radiant power; however, one needs to know more details than the PE to infer limiting factors in device performance.

The PE can be decomposed into its constituent factors, which are the voltage efficiency (VE), ηVE, and the external quantum efficiency (EQE), ηEQE. The EQE is then

*Corresponding author: Dong-Soo Shin, Department of Photonics and Nanoelectronics, Hanyang University ERICA, Ansan, Gyeonggi-do 15588, Republic of Korea; and Department of Bionanotechnology, Hanyang University ERICA, Ansan, Gyeonggi-do 15588, Republic of Korea, e-mail: [email protected]. http://orcid.org/0000-0002-0863-9138Jong-In Shim: Department of Photonics and Nanoelectronics, Hanyang University ERICA, Ansan, Gyeonggi-do 15588, Republic of Korea. https://orcid.org/0000-0002-1305-074X

Open Access. © 2018 Dong-Soo Shin et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 License.

https://doi.org/10.1515/nanoph-2018-0094

mailto:[email protected]

http://orcid.org/0000-0002-0863-9138

https://orcid.org/0000-0002-1305-074X

1602 J.-I. Shim and D.-S. Shin: Measuring the internal quantum efficiency of light-emitting diodes

decomposed into the light-extraction efficiency (LEE), ηLEE, and the internal quantum efficiency (IQE), ηIQE. The IQE is in turn separated into the injection efficiency (IE), ηIE, and the radiative efficiency (RE), ηRE. In formula, they are expressed as follows:

PE VE EQE

VE LEE IQE

VE LEE IE RE.

η η η

η η η

η η η η

= ⋅= ⋅ ⋅= ⋅ ⋅ ⋅

(1)

One can also define the active efficiency (AE), ηAE, by multiplying the VE and the IQE, i.e. ηAE = ηVE · ηIQE, to characterize the overall performance of the active layer. The definitions of the efficiencies mentioned above are summarized in Table 1. These efficiencies represent respective conversion processes in the LED [1–3].

The PE, VE, and EQE are measurable by using experi-mental data of current, voltage, radiant power, and spectra. On the other hand, measuring the IQE has been a constant challenge. Thus, measuring the IQE accurately and reliably is extremely useful not only to elucidate

the operating mechanisms of an LED device but also to improve the device performance.

2 Requirements for accurate and reliable IQE measurement

The first attempt to identify the IQE of an LED device is to theoretically calculate the LEE and measure the EQE as a function of DC bias current. Then the IQE is obtained by dividing the measured EQE by the calculated LEE. However, the LEE is quite sensitive to the microscopic parameters such as the imaginary refractive index of each material, the layer structure, or the randomly textured surface [14–16]. Theoretical calculation of the LEE is limited to a specific case in practice. Thus, direct measurement of the LED IQE as a function of current is more practical and has been pursued actively since the advent of LEDs in 1960s.

The IQE of an LED is a key parameter that represents the quality of epitaxial layers and contains essential

Table 1: Definitions of various LED efficiencies.

Efficiency Definition

PE ηΦ

≡ = ePE

F F

radiant powerelectrical power V I

VE νη ≡ =VE

F

mean photon energy ,electron potential energy

hqV

e

e0

( )h

dd

hc d

νλλ

λλ

∞

Φ≡

Φ∫

EQE eEQE

F

# of photons emitted to free space per second# of electrons injected into the LED per second

hI q

νη

Φ≡ =

LEE eLEE

e, active

# of photons emitted to free space per second# of photons emitted from the active region per second

hh

νη

ν

Φ≡ =

Φ

IQE e, activeIQE

F

# of photons emitted from the active region per second# of electrons injected into the LED per second

hI q

νη

Φ≡ =

IE F, activeIE

F

# of electrons injected into the active region per second# of electrons injected into the LED per second

I qI q

η ≡ =

RE e, activeRE

F, active

# of photons emitted from the active region per second# of electrons injected into the active region per second

hI q

νη

Φ≡ =

AE ηΦ

≡ = e, activeAE

F F

radiant power emitted from the active region .electrical power V I

The PE is also known as the wall-plug efficiency; the VE is sometimes referred to as the electrical efficiency. Φe, Radiant power; VF, forward voltage; IF, forward current; q, elementary charge; h, Planck constant; ν, frequency; λ, wavelength; c, speed of light in vacuum; dΦe(λ)/dλ, spectral distribution; Φe, active, radiant power emitted from the active region; IF, active, forward current injected into the active region.

J.-I. Shim and D.-S. Shin: Measuring the internal quantum efficiency of light-emitting diodes 1603

information on operational mechanisms such as the electron-hole recombination rate, the defect density, and carrier transport. As seen in Table 1, the IQE, defined as the ratio of the number of internally emitted photons to the number of electrically injected electrons, is the product of the IE and the RE. The IQE varies with the operating condi-tions of forward injection current I and temperature T as expressed below:

IQE IE RE( , ) ( , ) ( , ).I T I T I Tη η η= ⋅ (2)

The IE is a measure of how many electrons recombine in the active region compared to the total electrons injected into an LED. It generally depends on the current level as well as the LED structure itself. The RE can be thought of as the ratio of the radiative recombination rate to the total recombination rate (i.e. the sum of the radiative and non-radiative recombination rates) in the active region. For an accurate estimation of the IQE, it is necessary to consider the IE and the RE separately and quantitatively.

The IQE measurement methods satisfying the fol-lowing requirements are desirable in view of accuracy, simplicity, reproducibility, and experimental system cost: (i) use only experimentally measurable physical quantities such as current and radiant power without assuming any physical parameters, e.g. chip sizes, epi-taxial layer structures, carrier recombination rates, and complex refractive indices; (ii) measure the relative radiant power rather than the absolute radiant power for reducing measurement errors; and (iii) use measurement conditions of operational temperature and pumping scheme. The electroluminescence (EL) at room tempera-ture is the most preferable combination compared with others. Finally, (iv) use CW pumping and its steady-state response of spontaneous emission, which eliminates the need for complicated and expensive experimental setups such as a short-pulse current driver, a high-speed pho-todetector, and an impedance matching technique for a good RF signal integrity.

In Section 3, we review the IQE measurement methods that have been popularly utilized so far, especially the methods based on temperature- dependent electrolumi-nescence (TDEL) and constant AB(C) models. The techni-cal problems involved in the conventional methods are deeply discussed. In order to overcome such limitations, a unique method of the IQE measurement, named as the room-temperature reference-point method (RTRM), has been proposed recently. The RTRM with its theoretical background is explained in Section 4. We then show an example of separately and quantitatively measuring LED efficiencies in Section 5 and finally conclude in Section 6.

3 Conventional IQE measurement methods: features and limitations

3.1 TDEL method

The TDEL method has been most popularly utilized with the longest history in the LED community and rec-ognized as a standard method for IQE determination of LEDs [17–23]. This is partly due to the fact that it needs only a set of experimental data composed of the rela-tive radiant power vs. forward current (Φe-I) at various temperatures including cryogenic temperatures. The disadvantage of the TDEL method is that it requires an expensive and very stable cryogenic system for long measurement time.

Two important assumptions are introduced in the TDEL method. The first is that the LEE is constant, inde-pendent of current and temperature, so that the EQE should be linearly proportional to the IQE for any I and T. This assumption enables finding the IQE at any I and T only by comparing the EQE in question with the EQE at a so-called reference current and temperature, Iref and Tref, at which the IQE is exactly known as ηIQE, ref. In general, the reference point of Iref and Tref is selected for ηIQE, ref = 1 such that both the IE and the RE must be 100% there. To find the reference point satisfying ηIE = ηRE = 1, the second assumption is used. At cryogenic tempera-tures, the nonradiative recombination centers in the active layer, which induce the Shockley-Read-Hall (SRH) recombination, are “frozen” and become inactive. More-over, the direct Auger recombination rate in conventional semiconductors decreases exponentially with decreasing temperature so that the contribution of the Auger recom-bination rate is also neglected at the reference point. By assuming that both the SRH and Auger recombination rates are negligibly small at cryogenic temperatures, the RE is considered as 100% [24, 25]. In general, the assump-tion of ηRE = 1 is experimentally confirmed by the fact that the peak EQEs at cryogenic temperatures do not increase further and maintain the maximum value with decreas-ing temperature.

With the RE of 100%, the EQE is linearly proportional to the IE so that the peak of the EQE should correspond to the maximum IE. In this method, the IE is also taken as 100% when it is experimentally confirmed that the peak value of the EQE does not vary with current in a limited range [19, 20]. As the reference point corresponding to an IQE of 100% is decided this way, the IQEs at other oper-ating conditions are determined by taking the ratio as shown below:


EQEIQE

EQE ref ref

( , )( , ) .

( , )I T

I TI T

ηη

η= (3)

Note that ηEQE can be a relative EQE obtained from the rela-tive radiant power since only the ratio is taken to obtain the IQE.

Next, we need to discuss a limitation in applying the TDEL method. Figure 1A and B shows different shapes of the relative EQE curves as a function of forward current at various temperatures for two blue LED samples. The samples are commercial LEDs from two different companies, both with lateral electrodes. The chip sizes and dominant wavelengths are 290 × 590 μm2 and 458 nm for the sample shown in Figure 1A and 280 × 550 μm2 and 447 nm for the one in Figure 1B. Figure 1A shows that the relative EQE maximum does not increase further at tem-peratures below 50 K. In this case, the IE and RE (thus IQE) can be assumed to be 100% and the IQE at operating conditions can be determined by Equation (3). However,

some samples do not show such behaviors at cryogenic temperatures. In Figure 1B, the relative EQE maximums keep varying with decreasing temperature: the maximum of the relative EQE curves occurs at 100 K and then starts to decrease at temperatures lower than 100 K. In this case, the assumptions mentioned above are not satisfied: the TDEL method is not applicable to the LED samples showing this kind of behavior. The behavior is caused by the carrier leakage still remaining via processes like tunneling even with decreasing temperature, making the assumption that the maximum IE at the lowest cryo-genic temperature is 100% invalid. This behavior is often observed with relatively highly defective samples. Thus, it is very important to note that the IQE determination by the TDEL method is not always possible: one must confirm whether the validity criterion with the relative EQE curves with temperature, as outlined above, is satisfied to apply the TDEL method to the LED sample under study.

Although the TDEL is a generally accepted method of measuring the IQE as a function of current only from the experimental EQE curves obtained at different tempera-tures ranging from room to cryogenic, it is very time- and labor-consuming. Lowering the temperature to cryogenic as low as ~20 K takes several hours using a helium closed-cycle system. Including preparation and actual measure-ments, the total testing would take a few hours. Thus, the needs for methods that can measure the IQE just at room temperature arise.

3.2 Constant ABC model

The simplest and the most popular method of the IQE measurement satisfying all the conditions of (i)–(iv) men-tioned in Section 2 is the constant ABC model [26–42]. The model is based on the carrier rate equation for the LED (thus the name “ABC model”). Assumptions behind the model are as follows: (a) All carriers are injected into the active layers and recombine there. Thus, the IE is implicitly assumed as 100% with a well-defined active volume Va. In this case, the IQE becomes identical to the RE. (b) Nonequi-librium concentrations of electrons and holes in the active layers are nearly equal to each other. (c) Three recombina-tion processes, i.e. the nonradiative SRH, radiative band-to-band, and nonradiative Auger recombinations, are considered and their recombination rates are expressed with the recombination coefficients A, B, and C, respec-tively, and carrier concentration N. Note that A, B, and C coefficients are considered as certain constants. (d) Again, the LEE is independent of the injection current. Thus, the IQE has the same shape as the EQE as a function of current.

10–7 10–6 10–5 10–4 10–3 10–2 10–10

20

40

60

80

100A

B

Current (A)

10–7 10–6 10–5 10–4 10–3 10–2 10–1

Current (A)

25 K50 K

100 K200 K300 K

0

20

40

60

80

100

25 K50 K

100 K200 K300 K

Rel

ativ

e E

QE

(%

)R

elat

ive

EQ

E (

%)

Figure 1: Two different relative EQE curves as a function of current at various temperatures: In (A), the EQE peaks saturate with decreasing temperature while in (B), they do not saturate.It is thought that ηIQE = ηIE = ηRE = 1 in (A) while ηIQE ≠ 1 (ηIE ≠ 1) in (B) at their maximum EQE points.


In the constant ABC model, a few noticeable results have been theoretically derived. First, the IQE or the EQE dependence on the injection current I is analytically expressed with two fitting parameters, the maximum IQE value, ηmax, and the current, Imax, corresponding to ηmax as follows [42]:

max max

EQE EQE EQEmax max max

(1 )1 1 ,2

III I

ηη η η

η η

− = − +

(4)

where ηE̅QE = (Φe/I)/(Φe, max/Imax) and Φe and Φe, max are radiant powers measured at currents I and Imax, respec-tively. Note that Equation (4) has no explicit dependence on the A, B, and C coefficients and is unambiguously determined only by Imax and ηmax values where ηmax and Imax satisfy the condition of dηIQE/dI = 0. Since Imax is easily found experimentally by using the EQE vs. current rela-tion, ηmax is the only fitting parameter in Equation (4) in practice.

Second, A, B, and C coefficients are related to each other by ηmax and Imax as

22 3max

2 2 2max max max max

4 4 and ,(1 ) (1 )

k kB A C AI I

η

η η= =

− − (5)

where k = qVa/ηIE. Therefore, if one of the A, B, and C coefficients is known, the remaining coefficients can be obtained by using Equation (5) with the known quanti-ties of ηmax, Imax, and k. This is quite an unexpected result because A, B, and C constants represent different recombi-nation processes, independent of each other.

The next task is to determine the maximum IQE value, ηmax in Equation (4). Here, we introduce two approaches. The first is to select ηmax that gives the best fit between the normalized experimental EQE and the simulated curves by Equation (4). The second approach of finding ηmax is similar to the first: Equation (4) is rewritten as

1 2 1 2e e

max maxEQE

1 , ,2 2

QQ Q

Φ Φη η

η

−+= + =

+ + (6)

where Φ̅ e = Φe/Φe, max is the radiant power normalized by the peak EQE value. The factor Q B AC= is a dimension-less invariant parameter and simply called Q factor. η̅EQE and Φ̅e are experimental values of the EQE and the radiant power normalized by respective peak values. Plotting 1/ηE̅QE vs. 1 2 1 2

e e ,Φ Φ−+ approximating the plot by a linear function, and finding the intercept point of the line with the vertical axis, one can obtain the maximum IQE, ηmax, and subsequently the Q factor [28, 37, 38].

The accuracy of the constant ABC model largely depends on finding an exact value of ηmax so that a best fitting is usually taken around the EQE peak or Imax. However, one can often see that the data deviations from the ABC model predictions occur either at lower or higher currents from Imax. The mechanisms tentatively responsible for low- and high-current deviations from the ABC model predictions are introduced in detail in Refs. [35–42].

Apart from experimental discrepancies, the ABC model has a few theoretical limitations to be a reliable IQE measurement method. It should be remembered that this analysis is extremely dependent on many assumptions that are unverified in real-world devices. Some neglected complications can significantly alter the shape of the EQE curve and, thus, the parameter determination. The most suspicious assumptions are the following: (a) A, B, and C coefficients are not really constants but dependent on carrier concentration N and (b) the IE is not 100% but a function of current. Consequently, it is necessary to over-come theoretically and experimentally these technical hurdles arising from the constant ABC model for con-sistent and reliable measurement of the IQE values as a function of current.

3.3 Constant AB model

Two types of carrier losses related to the IE have been known: (i) nonradiative recombination through defects in the active layers and at the boundaries of the active layers (interfaces and surfaces) and (ii) leakage out of the active layers, i.e. carrier overflow. Usually, the two losses become important at low current levels far below the EQE peak and at high current levels beyond the EQE peak, respectively. In order to estimate the IQE exactly, each carrier loss needs to be identified quantitatively or at least relatively. However, the disentanglement of carrier losses into these two types is usually very diffi-cult [42–45].

The restriction of the universal usage of the constant ABC model comes from the fact that the dominant non-radiative recombination process considered in the model at high current levels includes only the Auger recombina-tion without identifying the influence of carrier overflow, i.e. the IE of 100% is always assumed with a well-defined active volume [41, 42]. Unfortunately, a method of discrim-inating between the Auger recombination and the carrier overflow experimentally is still controversial [36, 37].

The constant AB model has been developed in order to eliminate such an unclear problem of the IE at


high current levels involved in the constant ABC model [43–48]. The constant AB model is applied at low current levels around the onset of spontaneous emission in which the carrier loss of type (i) mentioned above becomes much more important than the carrier loss of type (ii). The crucial point is that all the losses of type (i) are thought to be directly proportional to the carrier concentration N in this regime. This means that all these losses can be lumped together in a single overall proportionality con-stant, or in a single effective nonradiative carrier lifetime τnr, which is independent of N. A simple theory shows that this approximation is reasonable when all the carrier recombination losses of type (i) have constant “saturated” recombination rates with a well-defined active volume. In this AB model, only an effective nonradiative recombina-tion with a constant recombination coefficient A and the radiative recombination with another constant coefficient B are accounted for, under the assumption of an IE of 100% at low currents.

The fitting procedure from the experimental EQE curve as a function of current has been reported origi-nally in Ref. [43] and recently in Ref. [47]. In this scheme, the IQE of an LED can be estimated from

1 2e, 12

IQE 1 2 1 20.5 e, 12

,Φ

ηΦ Φ

=+

(7)

where

EQE,2 EQE,1 e,1 e,20.5 e,12

EQE,1 e,1 EQE,2 e,2

and .2

η η Φ ΦΦ Φ

η Φ η Φ

− += =

−

(8)

In Equations (7) and (8), Φe = ηLEEhν̅VaBN 2 is the radiant power of the LED with the active volume Va and nonequi-librium electron/hole concentration N. Φ0.5 = ηLEEhν̅VaA2B−1 is the radiant power corresponding to an IQE of 50%. ηEQE, j and Φe, j, where j = 1, 2, are the EQE and the radiant power of the LED measured at two different driving currents. Just for an IQE, it is not necessary for ηEQE, j to be an absolute value. However, if the LEE is to be found, the absolute EQE value is required.

The constant AB model works well in some advanced LEDs where all the carrier losses of type (i) are so small that they are easily saturated at very small currents [46]. In reality, however, there are still many LED chips that have large and unsaturated carrier losses of type (i). Therefore, it is necessary to check the assumptions of an IE of 100% and the constancy of A and B recombina-tion coefficients before applying the constant AB model [48–50].

4 The RTRM

4.1 Theoretical background of the RTRM

The RTRM is a method to solve the technical problems in the constant ABC and AB models [51]. This improved model includes the following elements: (a) the recom-bination coefficients of A, B, and C are not constant but depends on the carrier concentration N; (b) the nonradia-tive Auger recombination is negligibly small at low cur-rents below from the maximum EQE current, Imax. In this current range, the AB model instead of the ABC model is possible; (c) the IE is a function of current I or carrier con-centration N so that there is a certain current, called the reference current Iref, where the IE is maximized; and (d) the LEE is assumed as constant so that the shape of an experimentally observed EQE curve is the same as that of the IQE curve. Thus, the IQE dependence on current can be obtained once an IQE is exactly known at one point of the reference current Iref. This approach is very similar to the TDEL where operating conditions of the current and cryogenic temperature are searched for the IQE to be assumed as 100%; and (e) the IE at Iref is considered as high as 100% if any special attention is not required.

In the AB model, the spontaneous radiant power detected by a photodetector Φe and the injection current I can be epxresssed by a simple quadratic equation as shown below:

2

1 2 ,Y a X a X= + (9)

where Y = I/Ip, e e max( ) / ( ).X I IΦ Φ= The a1 and a2 coefficients are dependent on current I and are given by

1 1 2 2

IE IE

1 ( ) 1( ) and ( ) ,( ) ( )( )

A Ia I K a I KI IB I η η

= = (10)

where K1 and K2 are constants. All other parameters of X, Y, a1, a2, A, B, and ηIE are functions of current I. Note that both X and Y are experimentally obtained parameters.

Here, we consider two paths of carrier losses recom-bining outside the active layers: (i) defect-related leakage current Idefect via surface, hetero-interface, or other defec-tive areas and (ii) overflow leakage current Ioverflow sur-passing the active layers. These leakage currents result in the IE not being ideal. As the forward voltage increases, the defect-related leakage current Idefect appears at low bias voltages and saturates at a finite density of trapping centers. Then, most of the carriers begin to inject into the active layers and recombine there with the IE increasing. As the bias voltage increases further, Ioverflow starts to flow


at a certain bias and becomes a dominant leakage-current component over Idefect, which in turn decreases the IE again. In this picture, there will be a certain current, called the reference current Iref, at which the IE is maximized.

Our idea to find Iref is as follows: As the current I increases, a1 and a2 generally vary very slowly compared to X and Y. Thus, the functions a1 and a2 are obtained by solving two simultaneous equations of (9) with two nearest experimental data (Xi, Yi) and (Xi+1, Yi+1). In Equation (10), the a2 coefficient is inversely proportional only to the IE. Thus, we select Iref as a current at which a2 is the minimum.

As a first step, we assume ηIE = 1 at I = Iref in that Idefect saturates at a much smaller current than Iref, i.e. Idefect < < Iref and Ioverflow is not so large yet. The IQE estimation errors due to this assumption is discussed in the next section. ηRE(Iref) is then found for the set of (Xref, a1, ref, a2, ref) at Iref, using ηRE = a2X2/(a1X + a2X2). Subsequently, ηIQE at Iref, i.e. ηIQE(Iref), is obtained by using already known values of ηIE = 1 at Iref.

Finally, we can calculate ηIQE(I) at any current I with a known value of ηIQE(Iref) from

EQEIQE IQE ref

EQE ref

( )( ) ( ) .

( )I

I II

ηη η

η= (11)

Table 2 summarizes the IQE measurement methods discussed so far.

4.2 The RTRM vs. TDEL and constant ABC model: comparison

We apply three IQE measurement methods of the TDEL, the constant ABC model, and the RTRM to a same blue LED chip and compare the results. A commercial lat-eral-type InGaN/GaN multiple-quantum-well blue LED grown on a c-plane sapphire substrate with a chip size of 1100 × 650 μm2 has been selected.

The LED was driven under the pulsed-current driving condition (pulse period: 1 ms, duty cycle: 1%) for minimum self heating. The LED sample was cooled down from 300 to 20 K in a helium closed-cycle cryostat by Advanced Research System.

Radiant powers from the sample measured at various temperatures are shown in Figure 2. The maximum radiant power at 250 mA is obtained at a medium temperature of 200 K, not at the lowest cryogenic temperature of 20 K, which is due to efficiency droops acting differently with current and temperature. Shown in Figure 3A are emission

Table 2: Summary of IQE measurement methods utilizing the electrical pumping and DC response.

Method IQE measurement procedure Notes

Calculation of LEE – Calculate the LEE– Measure the absolute EQE– Calculate the IQE (=EQE/LEE)

– Structural and material parameters are assumed

– Absolute EQE measurement at room temperature

TDEL – Measure the relative EQE curves at various temperatures including cryogenic temperatures

– Find a reference IQE at saturated peak EQEs– Calculate the IQE at room temperature

– Relative EQE measurements at various temperatures

– ηIQE = ηIE = ηRE = 1 at saturated EQE peaks– Constant LEE over temperatures and

currents

Constant ABC model – Measure the relative EQE curve– Find a peak IQE or constant ABC coefficients by best fitting the EQE curve– Calculate the IQE

– Relative EQE measurement at room temperature

– Constant A, B, C; ηIE = 1– Constant LEE over currents

Constant AB model – Measure the relative EQE curve– Find the LEE or AB coefficients by best fitting the EQE curve– Calculate the IQE


– Constant A, B; ηIE = 1– Constant LEE over currents

RTRM – Measure the relative EQE curve at room temperature– Find the IQE just at a reference point– Calculate the IQE curve


– ηIE = 1 just at a reference point– Constant LEE over currents


spectra on a linear scale at a current of 250 mA for various temperatures. As temperature decreases from 300 K to 200, 100, and 20 K, the peak wavelength shows the U-like shift from 448 nm to 445, 444, and 445 nm, respectively. We believe that this U-like shift of the peak wavelength is due to a tradeoff between the bandgap widening and the

thermal heating by increasing resistance. It is also seen that a subpeak around 460 nm becomes more pronounced. Actually, there are a series of subpeaks when the emission spectra are plotted on a log scale (Figure 3B). The more pronounced subpeaks with decreasing temperature have been reported as the longitudinal-optical (LO) phonon replicas of the main peak [52, 53]. On the other hand, an LED chip has finite reflectivities at the interfaces between metallic surfaces, epitaxial layers, and substrate surfaces. Since the optical losses are reduced with decreasing tem-perature, the Fabry-Perot effect is another possibility of the subpeaks. More investigation is necessary to further identify the exact cause of the subpeaks.

The I-V characteristics measured at various tempera-tures are depicted in Figure 4. It is seen in the reverse-bias region that the generation currents via defects at reverse biases less than −5 V are negligible at all temperatures and become smaller with decreasing temperature. On the other hand, it is not easy in the forward-bias region to identify the amount of leakage currents that do not recombine in the active layers. Here, we follow the RTRM in order to find the leakage current at relatively low current levels.

Figure 5 depicts a2 obtained by solving two simultane-ous equations for two nearest experimental data from the converted X-Y graph according to Equations (9) and (10). For this sample, the obtained a2 is not constant, implying that ηIE ≠ 1 over the current ranges investigated. At 300 K, a2 decreases for currents beyond ~10−5 A, approaches a minimum at 2 × 10−3 A (=Iref), and then increases. This indi-cates that the IE, inversely proportional to a2, approaches a maximum, which is considered as 100%, and then decreases. For very small currents below ~10−5 A denoted as region I, the rapid change in a2 could be due to the leakage current Idefect before the onset of the radiative current flowing into the active layers. It should be noted that such

400 420 440 460 480 500 5200.0

0.2

0.4

0.6

0.8

Nor

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ized

inte

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(a.

u.)

Nor

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ized

inte

nsity

(a.

u.)

1.0A

B

Wavelength (nm)

300 K200 K100 K

20 K

I = 250 mA

400 420 440 460 480 500 520

10–2

10–1

100

Wavelength (nm)

300 K200 K100 K

20 K

I = 250 mA

Figure 3: The peak wavelength shows the U-like shift as temperature decreases.Normalized intensities on (A) linear and (B) log scales measured at various temperatures.

–8 –6 –4 –2 0 2 410–10

10–9

10–8

10–7

10–6

10–5

10–4

Cur

rent

(A

)

10–3

10–2

10–1

100

Voltage (V)

300 K200 K100 K

50 K20 K

Figure 4: I-V characteristics at various temperatures.

0.00 0.05 0.10 0.15 0.20 0.25 0.300

100

200

300

Rad

iant

pow

er (

mW

)

400

500

600

700

Current (A)

300 K 200 K 100 K 50 K 20 K

Figure 2: Radiant power vs. current of a blue LED sample measured at various temperatures.


a leakage current is different in each device and operating condition so that we should pay attention to the influence of the leakage on the IQE calculation in every IQE meas-urement. For a current range of 10−5–2 × 10−3 A, denoted as region II, a2 decreases and the IE increases. This is due to the saturated Idefect and the monotonic increase of the radia-tive current. For I > Iref as denoted in region III, the carrier overflow from the InGaN quantum wells to the p-GaN clad layer should be responsible for the increasing a2 and decreasing ηIE. As the temperature is decreased, it is seen that a2 becomes flattened near the minimum, indicating that ηIE does not vary as much as at room temperature. This is reasonable because ηIE is not expected to change much at cryogenic temperatures with vanishing leakage paths owing to the defect freeze-out. This trend is confirmed later with the TDEL measurements (Figure 6).

Figure 6 shows the measured IQEs as functions of current by applying the TDEL (solid lines) and the RTRM (symbols). The IQEs at the reference currents from

Equation (10) are estimated to be 0.876, 0.959, and 0.978 for 300, 150, and 20 K, respectively, and other IQE values are calculated by using Equation (11). The maximum EQE at the cryogenic temperature is selected as IQE of 100% (Iref = 2 × 10−5 A, Tref = 20 K in this case) and ηIQE(I, T) at any temperature T is calculated from Equation (3). In TDEL, one should pay attention to experimentally confirming the saturation characteristics of the maximum ηEQE at the reference point by changing both temperature and current. As shown in Figure 6 by solid lines, ηIQE > 99% are measured at certain current ranges (7 × 10−6–2 × 10−4 A for 20 K and 2 × 10−5–5 × 10−4 A for 50 K).

The calculation procedures of the two methods, the RTRM and the TDEL, are very similar once ηIQE at a refer-ence point is found. ηIQE’s at other currents are then calcu-lated from ηIQE at the reference point by taking the relative ratios from the experimental ηEQE values. Thus, the shapes of the IQE curves at a certain temperature by the two methods are identical except the peak IQE values. The maximum ηIQE’s by the TDEL and RTRM at 300 K are almost the same as 0.941 and 0.943, respectively. The maximum IQEs by the two different methods agree very well within 2% for all temperatures. The small discrepancy in the maximum ηIQE obtained by the two methods could occur from the measurement inaccuracies in radiant power as well as the temperature dependency of the LEE [23]. The LEE can vary with temperature especially when the energy of the spontaneous emission from the active layer of an LED is close to the bandgap energy or absorption edge of the surrounding materials. Variations in LEE with InGaN-based LEDs have been reported to be as much as 4–6% over temperatures from ~10 to 300 K [23, 54, 55].

Finally, we discuss the error involved in the RTRM by assuming ηIE = 1 at Iref. Using the data obtained at 300 K, the left axis of Figure 7 shows a2(Iref)/a2(I), which

10–6 10–5 10–4 10–3 10–2 10–10.8

0.9

1.0

1.1

1.2

1.3

1.4

150 K

50 K

200 K

300 K

a 2

Current (A)

100 K

I

Iref at 300 K

II III

Figure 5: Calculated a2 as a function of current for various temperatures.Iref at 300 K is the current giving the minimum value of a2 in region II.

10–8 10–7 10–6 10–5 10–4 10–3 10–2 10–1 100

0.2

0.4

0.6

0.8

1.0

300 K200 K100 K

50 K20 K

IQE

Current (A)

Figure 6: IQEs obtained by the RTRM (symbols) and TDEL (solid lines) at various temperatures.

10–5 10–4 10–3 10–20.7

0.8

0.9

a 2(I

ref)/

a 2(I

)

1.0

1.1

0.7

0.8

0.9

1.0

1.1

X = 0.0%

T = 300 KIref = 2 mA

1.0%

0.8%

0.6%

0.4%0.2%

Ileak = X of Iref

Current (A)

(I –

I lea

k)/I

Figure 7: Comparison of the IE obtained from a2 at 300 K (left axis) and the theoretical IE for constant Ileak (right axis).


represents the IE. On the right axis, the theoretical IE, that is, (I – Ileak)/I, is given for a constant leakage current Ileak: naturally, the theoretical IE quickly approaches unity as the total current increases. From the various ratio of Ileak to Iref, it is seen that the IE from a2 roughly follows the func-tional shape of the theoretical IE between the leakage of 0.4% and 0.6% of Iref. This indicates that at Iref, the IE is considered to be 99.4% in the worst case. From this exer-cise, we think that the assumption of ηIE = 1 is reasonable, with only a minimal error included. Samples with very high leakage currents, however, should be treated care-fully as they may not satisfy the assumption ηIE = 1 at Iref.

In fact, theoretical background of the constant AB model is quite similar to that of the RTRM except that the former utilizes a wide range of relatively low current levels with ηIE = 1 and the latter selects one reference current with ηIE = 1. Thus, the key is to find the current at which the assumption of ηIE = 1. In this sense, we can get a lot of information from the calculation of a2 as a function of current as demonstrated in Figure 5.

We also try to fit the experimental data measured at 300 K by using the constant ABC model [Equation (4)]. The sample under test has Imax = 15 mA so that we can the-oretically calculate the normalized EQE curve with ηmax as a fitting parameter and compare it with the one obtained from the experiment (Figure 8). It is seen that ηmax = 90% gives the best fit for the data near Imax. Still, deviations from the experimental data are observed for lower and higher currents than Imax.

Using the ηmax value obtained by this fitting, we plot the relative ratios of the SRH, radiative, and Auger recombination currents to the total current (Figure 9). At Iref = 2 mA of the RTRM, denoted by the dotted line, it is seen that the Auger recombination current in the con-stant ABC model is 1.6% of the total current. With this level of contribution of the Auger recombination, we

think that the Auger recombination term can be neglected for finding the reference point in the RTRM method. In fact, the Auger recombination current in the constant ABC model can correspond to the current leakage via carrier overflow in the RTRM for certain constant A and B coefficients. In this picture, this negligible Auger recom-bination current at Iref can be considered as another vin-dication that the carrier leakage can be neglected at the reference point in the RTRM.

We have compared three IQE measurement methods of the RTRM, the TDEL, and the constant ABC model. All three methods have been developed to utilize the experi-mentally measured EQE curve. In the TDEL, the IQE of 100% at a cryogenic temperature is found by changing both temperature and current for a simultaneous con-dition satisfaction of ηIE = ηRE = 1. The IQE at room tem-perature is then calculated by the relative ratio of the EQE values at room temperature to the cryogenic refer-ence point under the assumption of a constant LEE for all temperatures. In fact, the LEE of an LED may not be constant: it typically becomes smaller at higher tempera-ture. Moreover, the temperature dependence of the EQE becomes larger as the emission wavelength of an LED becomes longer from visible to infrared spectral ranges. This results from the increase of optical losses in epitaxial layers whose bandgap energies are not so much different from that of the active layer. Therefore, the TDEL can be recommended to be used for InGaN-based visible LEDs rather than longer-wavelength GaAs- or InP-based LEDs. On the other hand, the RTRM and the constant AB(C) models under a given temperature assume only the con-stant LEE with current, which is more reasonable than in the TDEL.

10–7 10–6 10–5 10–4 10–3 10–2 10–1 10010–4

10–3

10–2

10–1

Cur

rent

rat

io

100

101

SRH

Current (A)

Iref = 2 mA

Imax = 15 mA

T = 300 K

Radiative

Augerηmax = 90%

Figure 9: Ratio of the SRH, radiative, Auger recombination currents to the total current.

10–5 10–4 10–3 10–2 10–1 1000.2

0.4

0.6

0.8

1.0

T = 300 K

80%

85%

90%

ηmax = 95%

Current (A)

Experiment

Nor

mal

ized

EQ

E

Figure 8: Normalized IQEs by the RTRM and the constant ABC model.


The conventional constant AB(C) models roughly assume the IE of 100% for certain current ranges near the onset of light emission or the EQE peak. In real LEDs, however, it is hardly true that the IE is perfect since the leakage current via defects near the onset of light emission and the carrier overflow near the EQE peak are frequently observed. The RTRM overcomes such technical hurdles in the conventional AB(C) models. From this consideration, we think that the RTRM is the most accurate and reliable of all the methods considered herein.

5 Application of the RTRM

5.1 Various LED efficiency measurements

Here, we demonstrate how one can measure various LED efficiencies constituting the PE. As individual efficien-cies represent different physical processes, separating various efficiencies is very beneficial in remedying any problems and enhancing the performance of LED chips further. For this purpose, we prepared a commercial lat-eral-type InGaN/GaN multiple-quantum-well blue LED grown on a c-plane sapphire substrate with a chip size of 740 × 600 μm2. The peak wavelength is ~450 nm at 293 K. The LED was driven under the pulsed-current driving con-dition (pulse period: 1 ms, duty cycle: 1%) by a Keithley sourcemeter 2602B. The pulsed-current driving here is for avoiding the self-heating effect and is not essential for the IQE measurement by the RTRM: measurement of the radiant power by the CW current injection is also OK even though the chip is heated at high currents. The IQE measured under CW current injection may reflect the IQE in real operating conditions. If one wants to measure the intrinsic LED characteristics at a given chip temperature, however, the pulsed-current driving is recommended. The response of an LED operated under this pulsed-current injection is still considered as steady state since the pulse is relatively long (in the order of 1 ms).

In the following example, we measure the absolute radiant power, not the relative radiant power, since the PE, EQE, and LEE measurements require the absolute radiant power. If one wants to measure the IQE only, the measurement of the relative radiant power is sufficient.

Figure 10 is a flow chart of measuring various LED efficiencies separately and quantitatively. We follow each step and show how the measurement of each efficiency is possible.

First, the PE should be obtained from the radiant power (voltage) vs. current measurement (Figure 11). Once

the radiant power and forward voltage are obtained as a function of current, the PE can be evaluated by taking the ratio of the radiant power to the input electrical power, as depicted by line 1 in Figure 12.

Second, measure the emission spectra and calculate the mean photon energy as defined in Table 1. Figure 13A and B shows the emission spectra at various injection cur-rents and the mean photon energy thus obtained. Using definitions given in Table 1, calculate the EQE by taking the ratio of the number of photons emitted to free space per second to the number of electrons injected into the LED per second. The result is shown as line 2 in Figure 12.

Third, now calculate the VE by taking the ratio of the PE to the EQE, whose result is shown as line 3 in Figure 12. Note that at currents below ~20 mA, the VE exceeds 100%, indicating that the mean photon energy is actually larger than the electron potential energy supplied by the source,

ηPE =Φe

Measure the EQE:

Measure the VE:

Measure the IQE: RTRM

Calculate the LEE:

Measure the PE:VFIF

ηEQE =Φe/hν

IF/q

ηVE =ηPE

ηEQE

ηLEE =ηEQEηIQE

Figure 10: Flow chart for the LED efficiency measurements.

0.0 0.1 0.2 0.32.0

2.5

3.0

3.5

4.0

4.5

Current (A)

0.0

0.1

0.2

Rad

iant

pow

er (

W)

0.3

0.4

0.5V

olta

ge (

V)

Figure 11: Radiant power and forward voltage as a function of forward current.


the fact only possible when one includes thermal energy into account. At voltages lower than the mean photon energy divided by the elementary charge, the carriers are still injected into the active region with the help of thermal

energy in the lattice. This interesting phenomenon has been reported elsewhere by various names such as elec-troluminescent refrigeration, opto-thermistic cooling, or thermo-photonic cooling since the cooling of the lattice occurs when the carriers take away the thermal energy from the lattice and get injected into the junction [56–58].

Fourth, now one needs to measure the IQE accurately. Using the RTRM, the IQE is obtained as shown by line 4 in Figure 12.

Lastly, once the IQE is obtained, the LEE can be obtained by taking the ratio of the EQE to the IQE. The LEE thus obtained is ~66% (line 5 in Figure 12). The key LED efficiencies of PE, EQE, VE, IQE, and LEE have thus been measured separately and quantitatively, giving important information on the respective physical processes.

5.2 IQE vs. forward voltage

Although the performances of InGaN-based LEDs have sig-nificantly improved, a higher PE is still desired. Improv-ing the PE requires enhancing the EQE and reducing the forward voltage simultaneously. While it has been recog-nized experimentally that both the EQE and the forward voltage are interactively dependent on epitaxial growth conditions in some cases, they have so far been studied independently as the so-called “efficiency droop” and the ohmic problem.

To have a higher EQE, one needs to optimize the epi-taxial layer structure, especially the active layers. However, the variation in LEE can mask the actual changes in active layers and confuses the trends in EQE experiments. In order to avoid the confusion caused by the LEE variation and focus only on the active layer properties, one needs to use the IQE, not the EQE. At the same time, the changes in forward voltage with epitaxial-structure modification should also be tracked. With the reliable IQE measurement such as the RTRM, investigating the correlation between the IQE and the forward voltage has become possible.

We have tested 45 InGaN/GaN multiple-quantum-well blue LEDs with three different chip types, fabricated by a single company. The growth condition for the active epitaxial layers of each LED chip is slightly different. Figure 14 shows the relationship between the forward voltage and the IQE at a current density of 25 A/cm2. Although these LEDs have been fabricated by identi-cal processes, it is clear that there is an inverse relation between the IQE and the forward voltage for different sets of active-epitaxial-layer growth conditions. This is the first systematic experimental result that the forward voltage is not solely determined by ohmic resistance: the carrier

410 420 430 440 450 460 470 480 490 5000.000

0.002

0.004

0.006

0.008

Em

issi

on s

pect

rum

dis

trib

utio

n (W

/m)

Mea

n ph

oton

ene

rgy

(eV

)

0.010A

B

Wavelength (nm)

0.0 0.1 0.2 0.32.60

2.65

2.70

2.75

2.80

Current (A)

Figure 13: Below ~20 mA, the mean photon energy is larger than the electron potential energy supplied by the source.(A) Emission spectra in the current range of 1 μA to 350 mA and (B) the mean photon energy as a function of forward current.

0.0 0.1 0.2 0.30.0

0.2

0.4

0.6

Effi

cien

cy

0.8

1.0

Current (A)

1

2

54

3

Figure 12: LED efficiencies as a function of forward current.1: PE; 2: EQE; 3: VE; 4: IQE; 5: LEE.


recombination rate in the active region plays a key role in LED devices. More details on the physical origin behind this observation require further investigation.

6 ConclusionMeasuring the IQE has a key importance in character-izing the LED performance and finding the detailed information on the physical processes in the LED. While there have been conventional methods of measuring the LED IQE such as the TDEL and constant AB(C) models, they have clear limitations in applying the method for various LEDs owing to specific assumptions utilized to obtain the IQE values as reviewed in Section 3. For example, the method based on the constant ABC model cannot fit the experimental data away from the EQE peak, which is due to the very rough assumption that ηIE = 1 for all current ranges. The more advanced RTRM eliminates this assumption, thus making it possible to measure the IQE as a function of current accurately. Moreover, the RTRM can be applied easily and reliably since it requires only the relative EQE curve as a func-tion of current just at room temperature.

We have applied the RTRM method to a blue LED and obtained various LED efficiencies of PE, VE, EQE, IQE, and LEE. It has also been revealed experimentally that the forward voltage of LEDs has a close relationship with the IQE, thus the carrier recombination rate in the active region. An accurate and reliable measuring method of the LED IQE such as the RTRM should greatly help elucidate the operational mechanisms of LEDs and improve the device performance further.

Acknowledgments: This work was supported by the Technology Innovation Program (Grant 10065712) funded by the Ministry of Trade, Industry and Energy, Republic of Korea. The authors are grateful to Dr. Dong-Pyo Han, Mr. Chan-Hyoung Oh of Hanyang University, and Dr. Hyundon Jung of EtaMax for their useful discussions and experi-mental help.

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0.80 0.82 0.84 0.86 0.88 0.902.8

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Jong-In Shim and Dong-Soo Shin* Measuring the internal